I'll second what MetalChef said.
The drop in pitch when bending a string is inherent of the design of any floating tremolo, including an unmodified Floyd Rose.
A floating trem is a delicate system. It is balanced on two posts, being kept in center by the force of the strings on one side - and on the other side, the force of the springs in the back. When you do a bend, what you do is increase the pull from the strings, which makes the trem rise slightly and all your other strings will go flat. There's no way around this, short of modifying the guitar. An original Floyd will do it just as much as a licenced Floyd copy or a vintage floating Fender trem.
Just as MetalChef mentioned, there are two ways in which you can modify your guitar to avoid this.
Blocking the trem will still allow you to do dive bombs, but not pull up on it. Most people accomplish this by gluing a form fitted block of wood into the tremolo route - the block goes in between the sustain block of the Floyd and the guitar body. You then tighten the springs in the back until you can bend strings without having the rest going flat. The trem will be much more stable (since the sustain block is resting against the wood block in the back) and enables you to rest your hand on it without affecting pitch. I believe this is how Ed Van Halen sets up his trems. There's a permanent thread (with pictures) about blocking trems in the Q&A section of the Jackson message board:
http://www.jcfonline.com/ubb/noncgi/ultimatebb.php?ubb=get_topic;f=7;t=000013
The Hipshot Tremsetter is a device that tries to keep the bridge in the "zero" position. I've never tried it myself, but some people have reported good results with it. The bridge will probably be a lot stiffer than usual, but you'll still be able to pull up on it.
So far I've kept my Floyd floating without any further modifications. I just avoid doing things like blues bends with adjacently ringing strings. =P
'bane
